Information or entropy analysis of diversity is used extensively in community ecology, and has recently been exploited for prediction and analysis in molecular ecology and evolution. Information measures belong to a spectrum (or q profile) of measures whose contrasting properties provide a rich summary of diversity, including allelic richness (q=0), Shannon information (q=1), and heterozygosity (q=2). We present the merits of information measures for describing and forecasting molecular variation within and among groups, comparing forecasts with data, and evaluating underlying processes such as dispersal. Importantly, information measures directly link causal processes and divergence outcomes, have straightforward relationship to allele frequency differences (including monotonicity that q=2 lacks), and show additivity across hierarchical layers such as ecology, behaviour, cellular processes, and nongenetic inheritance.

Information Theory Broadens the Spectrum of Molecular Ecology and Evolution

Boreal forests are experiencing dramatic climate change, having warmed 1.0°-1.9°C over the last century. Yet forest regeneration practices are often still dictated by a fixed seed zone framework, in which seeds are both harvested from and planted into predefined areas. Our goal was to determine whether seedlings sourced from southern seed zones in Minnesota USA are already better adapted to northerly seed zones because of climate change. Bur oak (Quercus macrocarpa) and northern red oak (Quercus rubra) seedlings from two seed zones (i.e., tree ecotypes) were planted into 16 sites in two northern seed zones and measured for 3 yr. Our hypotheses were threefold: (1) tree species with more southern geographic distributions would thrive in northern forests where climate has already warmed substantially, (2) southern ecotypes of these species would have higher survival and growth than the northern ecotype in northern environments, and (3) natural selection would favor seedlings that expressed phenotypic and phenological traits characteristic of trees sourced from the more southern seed zone. For both species, survival was high (>93%), and southern ecotypes expressed traits consistent with our climate adaptation hypotheses. Ecotypic differences were especially evident for red oak; the southern ecotype had had higher survival, lower specific leaf area (SLA), faster height and diameter growth, and extended leaf phenology relative to the northern ecotype. Bur oak results were weaker, but the southern ecotype also had earlier budburst and lower SLA than the northern ecotype. Models based on the fixed seed zones failed to explain seedling performance as well as those with continuous predictors (e.g., climate and geographical position), suggesting that plant adaptations within current seed zone delineations do align with changing climate conditions. Adding support for this conclusion, natural selection favored traits expressed by the more southern tree ecotypes. Collectively, these results suggest that state seed sourcing guidelines should be reexamined to permit plantings across seed zones, a form of assisted migration. More extensive experiments (i.e., provenance trails) are necessary to make species-specific seed transfer guidelines that account for climate trends while also considering the precise geographic origin of seed sources.

https://esajournals.onlinelibrary.wiley.com/doi/epdf/10.1002/eap.2092

Assisted migration across fixed seed zones detects adaptation lags in two major North American tree species.

During the process of ecological speciation, reproductive isolation results from divergent natural selection and leads to a positive correlation between genetic divergence and adaptive phenotypic divergence, that is, isolation by adaptation (IBA). In natural populations, phenotypic differentiation is often autocorrelated with geographic distance, making IBA difficult to distinguish from the neutral expectation of isolation by distance (IBD). We examined these two alternatives in a dramatic case of clinal phenotypic variation in an Andean songbird, the Line-cheeked Spinetail (Cranioleuca antisiensis). At its geographic extremes, this species shows a near threefold difference in body mass (11.5 to 31.0 g) with marked plumage differences. We analysed phenotypic, environmental and genetic data (5,154 SNPs) from 172 individuals and 19 populations sampled along its linear distribution in the Andes. We found that body mass was tightly correlated with environmental temperature, consistent with local adaptation as per Bergmann's rule. Using a PST -FST analysis, we found additional support for natural selection driving body mass differentiation, but these results could also be explained by environment-mediated phenotypic plasticity. When we assessed the relative support for patterns of IBA and IBD using variance partitioning, we found that IBD was the best explanation for genetic differentiation along the cline. Adaptive phenotypic or environmental divergence can reduce gene flow, a pattern interpreted as evidence of ecological speciation's role in diversification. Our results provide a counterexample to this interpretation. Despite conditions conducive to ecological speciation, our results suggest that dramatic size and environmental differentiation within C. antisiensis are not limiting gene flow.

Isolation by distance, not incipient ecological speciation, explains genetic differentiation in an Andean songbird (Aves: Furnariidae: Cranioleuca antisiensis, Line-cheeked Spinetail) despite near threefold body size change across an environmental gradient

Shannon entropy H and related measures are increasingly used in molecular ecology and population genetics because (1) unlike measures based on heterozygosity or allele number, these measures weigh alleles in proportion to their population fraction, thus capturing a previously-ignored aspect of allele frequency distributions that may be important in many applications; (2) these measures connect directly to the rich predictive mathematics of information theory; (3) Shannon entropy is completely additive and has an explicitly hierarchical nature; and (4) Shannon entropy-based differentiation measures obey strong monotonicity properties that heterozygosity-based measures lack. We derive simple new expressions for the expected values of the Shannon entropy of the equilibrium allele distribution at a neutral locus in a single isolated population under two models of mutation: the infinite allele model and the stepwise mutation model. Surprisingly, this complex stochastic system for each model has an entropy expressable as a simple combination of well-known mathematical functions. Moreover, entropy- and heterozygosity-based measures for each model are linked by simple relationships that are shown by simulations to be approximately valid even far from equilibrium. We also identify a bridge between the two models of mutation. We apply our approach to subdivided populations which follow the finite island model, obtaining the Shannon entropy of the equilibrium allele distributions of the subpopulations and of the total population. We also derive the expected mutual information and normalized mutual information (“Shannon differentiation”) between subpopulations at equilibrium, and identify the model parameters that determine them. We apply our measures to data from the common starling (Sturnus vulgaris) in Australia. Our measures provide a test for neutrality that is robust to violations of equilibrium assumptions, as verified on real world data from starlings.

/pdf/expected-shannon-entropy-and-shannon-differentiation-between-3gxpb3fiuh.pdf

Expected Shannon Entropy and Shannon Differentiation between Subpopulations for Neutral Genes under the Finite Island Model

Oak species show a wide variation in morphological and physiological characters, and species boundaries between closely related species are often not clear-cut. Still, despite frequent interspecific gene flow, oaks maintain distinct morphological and physiological adaptations. In sympatric stands, spatial distribution of species with different ecological requirements is not random but constrained by soil and other microenvironmental factors. Pre-zygotic isolation (e.g. cross incompatibilities, asynchrony in flowering, pollen competition) and post-zygotic isolation (divergent selection) contribute to the maintenance of species integrity in sympatric oak stands. The antagonistic effects of interspecific gene flow and divergent selection are reflected in the low genetic differentiation between hybridizing oak species at most genomic regions interspersed by regions with signatures of divergent selection (outlier regions). In the near future, the availability of high-density genetic linkage maps anchored to scaffolds of a sequenced Q. robur genome will allow to characterize the underlying genes in these outlier regions and their putative role in reproductive isolation between species. Reciprocal transplant experiments of seedlings between parental environments can be used to characterize selection on outlier genes. High transferability of gene-based markers will enable comparative outlier screens in different oak species.

/pdf/interspecific-gene-flow-and-maintenance-of-species-integrity-1vfp1jwtl1.pdf

Interspecific gene flow and maintenance of species integrity in oaks

https://www.fs.fed.us/nrs/pubs/jrnl/2012/nrs_2012_gailing_002.pdf

Genetic comparisons between North American and European populations of Lumbricus terrestris L.

Hybridization is considered to play an important role in speciation and evolution. Given the predicted northward tree migration in the eastern USA due to the impact of climate change, hybridization between related species is expected to become more frequent due to overlapping distribution ranges in the future. Oak species are “hot spots” of contemporary hybridization, serving as model organisms in the development of ecological species concepts. Q. rubra L. and Q. ellipsoidalis E.J. Hill were selected as study species, since they show different ecological requirements but hybridize with each other where both species co-occur. To identify morphological species and differentiation patterns in this species pair in ten populations on the Upper Peninsula of Michigan we investigated both leaf morphological variation, and genetic variation at highly variable microsatellite markers. Cluster analyses using leaf morphological characters revealed two distinct clusters for directly measured leaf characters and three clusters when additionally leaf shape characters were considered. Two populations growing on dry and sandy sites and identified as Q. ellipsoidalis in the field and by genetic assignment analyses were differentiated from the other eight populations at leaf morphological characters. Strong and significant correlations of leaf morphological differences with genetic distances at microsatellite markers but not with geographic distances are consistent with a pattern of isolation by adaptation. Differentiation at genetic and leaf morphological characters between neighboring populations in contrasting environments suggested reproductive isolation between populations of different species, possibly as the result of divergent selection. More extensive sampling along the distribution range of both species and reciprocal transplant experiments between parental environments are necessary to better understand the role of interspecific gene flow and selection in the maintenance of species identity in red oak species (Quercus section Lobatae).

https://www.fs.fed.us/nrs/pubs/jrnl/2012/nrs_2012_gailing_001.pdf

Leaf morphological and genetic differentiation between Quercus rubra L. and Q. ellipsoidalis E.J. Hill populations in contrasting environments

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Genetic comparisons between North American and European populations of Lumbricus terrestris L.

Leaf morphological and genetic differentiation between Quercus rubra L. and Q. ellipsoidalis E.J. Hill populations in contrasting environments